The Landau equation does not blow up
Analysis of PDEs
2025-01-29 v2
Abstract
We consider solutions to the space-homogeneous Landau equation with a general family of interaction potentials. We prove that their Fisher information is monotone decreasing in time. The class of interaction potentials covered by our result includes the case of the Landau equation with Coulomb interactions. As a consequence of the global boundedness of the Fisher information, we deduce that solutions to the space-homogeneous Landau equation never blow up.
Cite
@article{arxiv.2311.09420,
title = {The Landau equation does not blow up},
author = {Nestor Guillen and Luis Silvestre},
journal= {arXiv preprint arXiv:2311.09420},
year = {2025}
}
Comments
In the second version, we added some references and fixed some trivial typos